Sets

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A set is a well-defined collection of distinct objects. The objects in a set are called elements. Sets are written by enclosing all elements between brackets { }. Example: Set of first five prime num…

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1. Roster Form (Listing Form): Elements are listed within curly brackets Example: A = {2, 4, 6, 8, 10} 2. Set-builder Form: Elements are defined by a common property Example: A = {x : x is an e…

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• ∈ (belongs to): Used when an element is in the set Example: 5 ∈ {1, 3, 5, 7, 9} • ∉ (does not belong to): Used when an element is not in the set Example: 6 ∉ {1, 3, 5, 7, 9}…

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An empty set (null set or void set) is a set that contains no elements. It is denoted by ∅ or { }. Examples: 1. {x : x is a natural number smaller than 1} 2. {x : x is an odd number divisible by 2} 3…

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A universal set is a set that contains all elements under consideration for a particular discussion. It is denoted by μ or U and represented by rectangles in Venn diagrams. Example: If we study natur…

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If all elements of set A are present in set B, then A is said to be a subset of B, denoted by A ⊆ B. A ⊆ B ⟺ "a ∈ A ⇒ a ∈ B" • ⊆ means 'subset of' • ⊂ means 'proper subset of' Every set is a subset…

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Two sets A and B are equal if every element in A belongs to B and every element in B belongs to A. Condition: A = B ⟺ A ⊆ B and B ⊆ A Example: A = {p, q, r} and B = {q, p, r} Since every element of …

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The union of sets A and B is the set of all elements that belong to A or B (or both). Formula: A ∪ B = {x : x ∈ A or x ∈ B} Example: If A = {1, 2, 3, 4} and B = {2, 4, 6, 8} Then A ∪ B = {1, 2, 3, 4…